This project involves mathematical, physical and statistical consulting in collaboration with other NIH scientists which require sophisticated techniques common in these disciplines. Three major projects are current. The first is that of writing a book with Dr. A. Szabo of the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) on models for reaction rates for reactions in solvents. A second project with members of NIDDK relate to the development of models for diffusion which account for both velocities and positions of particulate matter, in contrast to most current theory which takes only position into account. This has been carried out in collaboration with Dr. D.J. Bicout (NIDDK). Thus far, it has been shown that a physically useful theory can be developed in which particle velocity need only take on three discrete values. The third project relates to optical imaging techniques. Here, the focus of research has been on determining the statistical properties of photon trajectories in human tissue, i.e., what part of the tissue is probed by laser radiation commonly used in biomedical applications. Theory is required for this purpose in order to interpret experimental findings, and to associate these with physiologic features of the tissue. This research was mainly carried out in collaboration with Dr. A. Gandjbakhche of the National Institute of Child Health and Human Development (NICHD). A mathematical model for calcium absorption has been applied to interpret kinetic data on patients with osteogenesis imperfecta, to test whether it can discriminate between different disease stages. This has been proven to be the case. The work was carried out in collaboration with N. Vieira (NICHD) and other physicians working on this class of patients.